How to read blender API manual?
Don't worry, learning to read an API is a skillset unto itself, and a non-trivial endeavor at that, so it's okay for it to feel daunting. Unfortunately, it's usually necessary.

To answer your first question, ArmatureBones is a member of armature. It is a container, but it's not a built in Python container like list or tuple. It's a Blender container of type bpy_prop_collection, and this instance of that type of container contains Bones.

This would be roughly equivalent to saying "Encyclopedia is list of Books."

To answer your second question, there are a number of different types of context. Without knowing which one you're referencing it's hard to guess. However, there is a screen context, and it makes sense that a screen doesn't have an armature. So if you're referencing one of those other contexts, it'd make sense for it to has no attribute 'armature'.

Furthermore, the context that does have an armature is the buttons context, which means it's probably not the armature you're looking for. I suspect that you're actually after bpy.data.objects["name_of_your_rig"].data as referenced in this answer over here.

I hope that helps!